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There was an army hospital not too far from there that had a kind of cafeteria in its basement. It was a lunchroom with only vending machines. Hot and cold sandwiches, maybe soups, chips, drinks, etc. I can't remember if there was a special name for it. I think this might have been a throwback to an earlier era.

Is Automat what you are thinking of?
In addition to the famous Horn & Hardart, I think there was a Chock full o'Nuts Automat in Manhattan too. At any rate I ate at one or two of them as a yute.